Title data
Yegorov, Ivan ; Dower, Peter ; Grüne, Lars:
A characteristics based curseofdimensionalityfree approach for approximating control Lyapunov functions and feedback stabilization.
Bayreuth ; Melbourne
,
2018
.  8 S.
Project information
Project title: 



Project financing: 
ARC (Australian Research Council) AFOSR/AOARD 
Abstract
This paper develops a curseofdimensionalityfree numerical approach to construct control Lyapunov functions (CLFs) and stabilizing feedback strategies for deterministic con trol systems described by systems of ODEs. An extension of the Zubov method is used to represent a CLF as the value function for an appropriate infinitehorizon optimal control problem. The infinitehorizon stabilization problem is approximated by an exit time problem, with target set given by a sufficiently small closed neighborhood of the origin in the state space. In order to compute the related value function and optimal feedback control law separately at different initial states and thereby to attenuate the curse of dimensionality, an extension of a recently developed characteristics based framework is proposed. Theoretical foundations of the developed approach are given together with practical discussions regarding its implementation, and numerical examples are also provided. In particular, it is pointed out that the curse of complexity may remain a significant issue even if the curse of dimensionality is avoided.
Further data
Item Type:  Preprint, postprint 

Keywords:  control Lyapunov functions; optimal control; optimization; stabilization by feedback 
DDC Subjects:  500 Science > 510 Mathematics 
Institutions of the University:  Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics)  Univ.Prof. Dr. Lars Grüne Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics Profile Fields > Advanced Fields > Nonlinear Dynamics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Profile Fields Profile Fields > Advanced Fields 
Language:  English 
Originates at UBT:  Yes 
URN:  urn:nbn:de:bvb:703epub35770 
Date Deposited:  12 Feb 2018 07:40 
Last Modified:  28 Mar 2019 09:55 
URI:  https://epub.unibayreuth.de/id/eprint/3577 